pythagorean triple

The set of such points turns out to be closely related to primitive Pythagorean triples.

All Pythagorean triples may be found by this method.

There are several ways to generalize the concept of Pythagorean triples.

There are a number of results on the distribution of Pythagorean triples.

Pythagorean Triples are three whole numbers which meet the equation .

Pythagorean triples are found in Apastamba's rules for altar construction.

It follows that there are infinitely many primitive Pythagorean triples.

However, right triangles with non-integer sides do not form Pythagorean triples.

There is an infinite number of Pythagorean triples.

If n equals two, the equation has infinitely many solutions, the Pythagorean triples.

It consists of a table of cuneiform numbers, specifically Pythagorean triples.

However, if one allows for Pythagorean triples with rational entries, not necessarily integers, then the answer is affirmative.

The following will generate all Pythagorean triples uniquely:

There is therefore a correspondence between points on the unit circle with rational coordinates and primitive Pythagorean triples.

(See Pythagorean triples by use of matrices and linear transformations.)

There are several Pythagorean triples which are well-known, including those with sides in the ratios:

Besides Euclid's formula, many other formulas for generating Pythagorean triples have been developed.

See also Tree of primitive Pythagorean triples.

They contain lists of Pythagorean triples, which are particular cases of Diophantine equations.

In elementary arithmetic geometry, stereographic projection from the unit circle provides a means to describe all primitive Pythagorean triples.

The analytic method is ascribed to Plato, while a formula for obtaining Pythagorean triples bears his name.

This table lists what are now called Pythagorean triples, i.e., integers a, b, c satisfying .

This problem is related to the problem of finding Pythagorean triples, which appeared in the second millennium B.C.

The set of all primitive Pythagorean triples has the structure of a rooted tree, specifically a ternary tree, in a natural way.